Towards a classification of modular invariant partition functions for theories based onN=4 superconformal algebras

The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 385–394, May, 1993.